Semiconductor Electronics— Notes, Formulas & Revision

In a solid, atomic energy levels broaden into BANDS due to overlap of electron wavefunctions.

Valence band: highest filled (or partially filled) band at T = 0. Conduction band: next higher (mostly empty).

Energy gap E_g = bottom of conduction band − top of valence band.

Conductors: bands overlap or valence band partially filled ⇒ free electrons readily move. Eg ≈ 0.

Insulators: large gap (E_g > ~3 eV). Few electrons can be thermally excited to the CB.

Semiconductors: small gap (E_g ~ 0.5-2 eV). Some thermal excitation at room temperature.

Conduction in semiconductors involves BOTH electrons in CB and HOLES (missing electrons in VB) — holes act like positive charge carriers.

Doping creates extra states INSIDE the gap close to CB (donor → n-type) or VB (acceptor → p-type), dramatically changing conductivity.

CLASSIFICATION of solids by electrical conductivity / band structure:

Conductors (metals): partially filled or overlapping bands; resistivity ~10⁻⁸ Ω·m; conductivity DECREASES with temperature.

Insulators: large bandgap (E_g > 3 eV); resistivity 10⁸-10¹⁶ Ω·m; essentially no free carriers at room temperature.

Semiconductors: small bandgap (0.5-2 eV); resistivity 10⁻⁴-10⁴ Ω·m; conductivity INCREASES with temperature.

Conductivity range spans ~24 orders of magnitude across these classes — most extreme variation in all of solid-state physics.

Doping makes semiconductors functionally indispensable — controllable conductivity by orders of magnitude.

Examples: Cu, Ag, Au (conductors); diamond, rubber, glass (insulators); Si, Ge, GaAs (semiconductors).

An INTRINSIC semiconductor is pure — no dopants. Examples: ultra-pure Si and Ge.

At T = 0 K: VB fully filled, CB empty ⇒ behaves as insulator.

At room T: a few electrons thermally excited to CB, leaving an equal number of HOLES in VB ⇒ n = p = n_i.

Carrier density depends exponentially on temperature: n_i ∝ T^(3/2) · exp(−E_g/2k_BT).

For intrinsic Si at 300 K: n_i ≈ 1.5 × 10¹⁰/cm³. For Ge: ~2.4 × 10¹³/cm³.

Holes drift in the OPPOSITE direction to electrons in an applied field ⇒ both contribute to current in the SAME direction.

Intrinsic conductivity at room T is too small for practical devices ⇒ doping is essential.

Extrinsic semiconductor = intrinsic + dopants. Two types:

n-type: doped with Group V element (P, As, Sb) — has one EXTRA valence electron ⇒ donates to CB.

Donor level is just below CB. Even at low T, donors ionise easily ⇒ many free electrons.

p-type: doped with Group III (B, Ga, Al) — has one FEWER valence electron ⇒ creates HOLES in VB.

Acceptor level is just above VB. Electrons easily jump from VB to acceptor ⇒ many free holes.

Majority carriers: n-type → electrons; p-type → holes. Minority carriers are the opposite.

Mass-action law: n·p = n_i² always holds. In doped: one carrier is much larger than n_i, the other much smaller.

Doping concentrations are tiny (1 part per million or less) but change conductivity by ~10⁶ ×.

A p-n junction is formed by joining p-type and n-type semiconductors (in a single crystal, not metal contact).

Diffusion: electrons from n-side diffuse to p-side; holes from p-side diffuse to n-side. Diffusion currents flow.

Diffusion leaves IONISED dopants behind — a DEPLETION region (charge-depleted of mobile carriers) forms at the junction.

The ionised donors (positive) and acceptors (negative) create a built-in electric field that OPPOSES further diffusion ⇒ equilibrium.

Built-in potential V₀ (~0.6-0.7 V for Si, ~0.3 V for Ge) is the equilibrium contact potential.

Forward bias (p connected to +): reduces V₀ and depletion width ⇒ large current flows.

Reverse bias (p connected to −): increases V₀ and depletion width ⇒ tiny saturation current.

This asymmetry makes the p-n junction a DIODE — passes current one way, blocks the other.

A p-n junction diode has an asymmetric I-V curve: ALMOST NO current in reverse, EXPONENTIAL current in forward.

Forward characteristic: current is negligible until V ≈ V_threshold (knee voltage, ~0.7 V Si, ~0.3 V Ge), then rises steeply.

Reverse characteristic: tiny saturation current I₀ (nA-μA) until BREAKDOWN voltage, where current suddenly grows.

Static resistance R = V/I (depends on operating point). Dynamic (small-signal) resistance r_d = dV/dI = k_BT/(eI) at room temperature.

Ideal diode: zero forward resistance, infinite reverse resistance — used in idealized circuit analysis.

Real diode has a 'knee' due to V_threshold and finite forward slope (a few Ω).

Breakdown mechanisms: Zener (tunnelling, low V_BR, < 5V) and avalanche (impact ionisation, high V_BR).

Special diodes: LED (light emission), photodiode (photocurrent), Zener (voltage reference), Schottky (low V_F), tunnel diode.

Half-wave rectifier: a single diode in series with a load lets only one HALF of the AC cycle pass.

During the positive half of input AC: diode forward-biased, current flows.

During the negative half: diode reverse-biased, blocks current (output = 0).

Output is a series of positive pulses, not smooth DC.

Average (DC) output voltage: V_dc = V_m/π ≈ 0.318 V_m, where V_m is the input peak.

RMS output: V_rms = V_m/2 (over the full cycle).

Ripple factor (RMS of AC component / DC) for half-wave: ~1.21 — very poor; needs heavy filtering.

PIV (Peak Inverse Voltage) the diode must withstand: V_m.

Efficiency: ~40.6% — poor. Half-wave is used only when simplicity matters and load draws little current.

A full-wave rectifier inverts the negative half of the AC cycle, producing pulses for BOTH halves.

Two common topologies: (i) Centre-tapped transformer with 2 diodes; (ii) bridge rectifier with 4 diodes (no centre tap).

Output frequency = 2× input frequency (100 Hz from 50 Hz mains).

Average (DC) output: V_dc = 2V_m/π ≈ 0.637 V_m. DOUBLE that of half-wave.

RMS: V_rms = V_m/√2.

Ripple factor: γ ≈ 0.482 — much better than half-wave's 1.21.

Efficiency: ~81.2% — twice half-wave.

PIV: 2V_m for centre-tap; V_m for bridge. Bridge is preferred because diode rating is half — but uses 4 diodes.

Combined with a filter capacitor and (optionally) a voltage regulator, you get a usable DC supply.

A bipolar junction transistor (BJT) is a 3-terminal device with two p-n junctions: NPN or PNP. Terminals: Emitter (E), Base (B), Collector (C).

NPN transistor in 'active' mode: E-B junction forward-biased, C-B junction reverse-biased.

Emitter (heavily doped) injects electrons into Base (lightly doped, thin); most diffuse across to the Collector (moderately doped).

Small base current I_B controls large collector current I_C — transistor is a CURRENT AMPLIFIER.

Current gain β (or h_FE) = I_C/I_B; typically 50-300. α = I_C/I_E ≈ 0.99.

Three operating regions: (i) Cutoff (both junctions reverse, transistor OFF). (ii) Active (E-B forward, C-B reverse, amplifies). (iii) Saturation (both forward, transistor 'ON' as a switch).

Three common configurations: (i) Common-Emitter — high current AND voltage gain; (ii) Common-Base — voltage gain only; (iii) Common-Collector (emitter follower) — current gain, unity voltage gain, high input impedance.

Applications: amplifiers, switches, oscillators, logic gates. Modern MOSFETs (field-effect) dominate ICs.

Logic gates are circuits whose output depends on Boolean inputs (HIGH/1 or LOW/0). Building blocks of all digital systems.

Basic gates: AND, OR, NOT. Universal gates: NAND, NOR (any logic can be built from either alone).

Truth tables define each gate's behaviour. AND: output 1 only if all inputs 1. OR: output 1 if any input 1. NOT: inverts input.

XOR (exclusive OR): output 1 when inputs differ. XNOR: complement of XOR.

DeMorgan's laws: (A·B)' = A' + B' and (A+B)' = A'·B'. Lets you convert AND into OR (with inversions) and vice versa.

CMOS technology builds all logic from complementary p-MOS and n-MOS pairs — very low static power consumption.

Standard CMOS voltages: V_DD = 3.3 V or 5 V; logic 0 < ~0.8 V, logic 1 > ~2.0 V (TTL levels).

Combinational logic: output depends only on current inputs (adders, multiplexers). Sequential logic: output also depends on past (flip-flops, registers, memory).

A Zener diode is a heavily-doped p-n junction designed to operate in REVERSE BREAKDOWN.

Below breakdown: behaves like normal diode (low reverse current).

At V = V_Z (Zener voltage): reverse current suddenly grows, but voltage stays nearly constant.

This sharp clamp at V_Z is exploited for VOLTAGE REGULATION — line voltage or load may vary, output stays at V_Z.

Breakdown mechanisms: Zener effect (tunnelling, V_Z < ~5 V, has negative T-coefficient) vs avalanche (impact ionisation, V_Z > ~5 V, positive T-coefficient). At ~5 V both contribute and T-coefficient is minimal — used in temperature-stable references.

Always operate with a SERIES RESISTOR to limit current. Otherwise the diode burns out at breakdown.

Used in: voltage regulators, surge protectors, waveform clippers, reference voltages.

Light-Emitting Diode (LED) = a forward-biased p-n junction (made of a direct-bandgap semiconductor) that emits light when electrons recombine with holes in the depletion region.

Emitted photon energy ≈ E_g of the semiconductor ⇒ λ = hc/E_g.

Material chooses colour: GaAs (IR, λ ~ 870 nm), GaAsP (red), GaP (green), GaN/InGaN (blue-UV), GaN+phosphor (white).

Direct-bandgap materials (GaAs, GaN) make efficient LEDs; indirect-bandgap (Si) emit very little light.

Forward voltage V_F depends on colour: red ~1.8 V, green ~2.2 V, blue ~3.0 V, UV ~3.5+ V.

LED current must be limited externally (resistor or constant-current driver) — they have negative dynamic resistance.

Efficiency: modern white LEDs reach 100-200 lm/W (vs incandescent ~15 lm/W).

Applications: indicator lights, displays, traffic signals, solid-state lighting, fibre-optic communications, OLED displays.